[R] complex contrasts and logistic regression

[Frank E Harrell Jr]

Nicholas Lewin-Koh wrote:
> Hi,
> I am doing a retrospective analysis on a cohort from a designed trial,
> and I am fitting
> the model
> 
> fit<-glmD(survived ~ Covariate*Therapy + confounder,myDat,X=TRUE,
> Y=TRUE, family=binomial()) 

For logistic regression you can also use Design's lrm function which 
gives you more options.

> 
> My covariate has three levels ("A","B" and "C") and therapy has two
> (treated and control), confounder is a continuous variable.
> Also patients were randomized to treatment in the trial, but Covariate
> is something that is measured
> posthoc and can vary in the population.

If by posthoc you mean that the covariate is measured after baseline, it 
is difficult to get an interpretable analysis.

>  
> I am trying to wrap my head around how to calculate a few quantities
> from the model
> and get reasonable confidence intervals for them, namely I would like to
> test
> 
> H0: gamma=0, where gamma is the regression coefficient of the odds
> ratios of surviving
>              under treatment vs control at each level of Covariate
>              (adjusted for the confounder)

You mean regression coefficient on the log odds ratio scale.  This is 
easy to do with the contrast( ) function in Design.  Do ?contrast.Design 
for details and examples.

> 
> and I would like to get the odds of surviving at each level of Covariate
> under treatment and control
> for each level of covariate adjusted for the confounder. I have looked
> at contrast in the Design 
> library but I don't think it gives me the right quantity, for instance 
> 
> contrast(fit,list(covariate="A", Therapy="Treated",
> confounder=median(myDat$confounder), X=TRUE)
> ( "A" is the baseline level of Covariate) 
> 
> gives me beta0 + beta_Treated + beta_confounder*68  
> 
> Is this correctly interpreted as the conditional odds of dying? 
> As to the 1st contrast I am not sure how to get it, would it be using
> type = 'average' with some weights 
> in contrast? The answers are probably staring me in the face, i am just
> not seeing them today.

contrast( ) is for contrasts (differences).  Sounds like you want 
predicted values.  Do ?predict  ?predict.lrm  ?predict.Design.  Also do 
?gendata which will generate a data frame for getting predictors, with 
unspecified predictors set to reference values such as medians.

Frank

> 
> Nicholas
> 
> 
> 


-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University